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Characterization of vector-valued $L^1$-$L^p$ multipliers for Weyl transform

Ritika Singhal, N. Shravan Kumar

Abstract

In this article, we will characterize Weyl multipliers for the pair $(L^1(G \times \widehat{G}; A), L^p(G \times \widehat{G};A))$, for $1 \leq p< \infty$, under the assumption that $A$ is a complex Banach algebra with a bounded approximate identity.

Characterization of vector-valued $L^1$-$L^p$ multipliers for Weyl transform

Abstract

In this article, we will characterize Weyl multipliers for the pair , for , under the assumption that is a complex Banach algebra with a bounded approximate identity.

Paper Structure

This paper contains 4 sections, 12 theorems, 57 equations.

Table of Contents

  1. Introduction
  2. Preliminaries
  3. Characterization of $L^1(G \times \widehat{G}; A)$ Weyl multipliers
  4. Characterization of $L^1(G \times \widehat{G}; A)$-$L^p(G \times \widehat{G}; A)$ Weyl multipliers

Key Result

Theorem 1.1

Let $G$ be a locally compact abelian group, and suppose $T: L^1(G) \rightarrow L^1(G)$ is a continuous linear transformation. Then the following are equivalent:

Theorems & Definitions (21)

  • Theorem 1.1: MR435738, Theorem 0.1.1
  • Theorem 2.1
  • Lemma 2.2
  • proof
  • Lemma 2.3: aren
  • Theorem 2.4
  • Definition 2.5
  • Proposition 2.6
  • proof
  • Lemma 3.1
  • ...and 11 more